Aptitude - Numbers

Exercise :: Numbers - General Questions

71. 

397 x 397 + 104 x 104 + 2 x 397 x 104 = ?

A. 250001
B. 251001
C. 260101
D. 261001

Answer: Option B

Explanation:

Given Exp. = (397)2 + (104)2 + 2 x 397 x 104
= (397 + 104)2
= (501)2 = (500 + 1)2
= (5002) + (1)2 + (2 x 500 x 1)
= 250000 + 1 + 1000
= 251001

72. 

(35423 + 7164 + 41720) - (317 x 89) = ?

A. 28213
B. 84307
C. 50694
D. 56094
E. None of these

Answer: Option D

Explanation:

  35423         317 x 89 = 317 x (90 -1 )
+  7164                  = (317 x 90 - 317)
+ 41720                  = (28530 - 317)
  -----                  = 28213
  84307
- 28213
  -----
  56094
  -----

73. 

(xn - an) is completely divisible by (x - a), when

A. n is any natural number
B. n is an even natural number
C. n is and odd natural number
D. n is prime

Answer: Option A

Explanation:

For every natural number n, (xn - an) is completely divisible by (x - a).


74. 

Which one of the following numbers is completely divisible by 45?

A. 181560
B. 331145
C. 202860
D. 2033555
E. None of these

Answer: Option C

Explanation:

45 = 5 x 9, where 5 and 9 are co-primes.

Unit digit must be 0 or 5 and sum of digits must be divisible by 9.

Among given numbers, such number is 202860.


75. 

Which of the following numbers will completely divide (325 + 326 + 327 + 328) ?

A. 11
B. 16
C. 25
D. 30

Answer: Option D

Explanation:

(325 + 326 + 327 + 328) = 325 x (1 + 3 + 32 + 33) = 325 x 40

     = 324 x 3 x 4 x 10

     = (324 x 4 x 30), which is divisible by30.


76. 

A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:

A.
B. 1
C. 2
D. 3

Answer: Option D

Explanation:

Let x = 6q + 3.

Then, x2 = (6q + 3)2

   = 36q2 + 36q + 9

   = 6(6q2 + 6q + 1) + 3

Thus, when x2 is divided by 6, then remainder = 3.


77. 

The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?

A.
12
35
B.
1
35
C.
35
8
D.
7
32

Answer: Option A

Explanation:

Let the numbers be a and b. Then, a + b = 12 and ab = 35.

a + b = 12          1 + 1 = 12
ab 35 b a 35

Sum of reciprocals of given numbers = 12
35


78. 

What will be remainder when 17200 is divided by 18 ?

A. 17
B. 16
C. 1
D. 2

Answer: Option C

Explanation:

When n is even. (xn - an) is completely divisibly by (x + a)

(17200 - 1200) is completely divisible by (17 + 1), i.e., 18.

   (17200 - 1) is completely divisible by 18.

   On dividing 17200 by 18, we get 1 as remainder.


79. 

If 1400 x x = 1050. Then, x = ?

A.
1
4
B.
3
5
C.
2
3
D.
3
4
E. None of these

Answer: Option D

Explanation:

1400 x x = 1050      x = 1050 = 3
1400 4

80. 

(12 + 22 + 32 + ... + 102) = ?

A. 330
B. 345
C. 365
D. 385

Answer: Option D

Explanation:

We know that (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1)
6

Putting n = 10, required sum = 1 x 10 x 11 x 21 = 385
6